I installed by downloading the .tar.bz2 file from the Azureus site on sourceforge to a "download" directory in my home directory. From that download directory, I uncompressed the file which created a new "azureus" directory in my "download" directory. I went in the "azureus" directory, and read "README.txt" which stated:
Azureus requires Sun Java 1.4.x or newer to run.
JRE 1.5 (5.0 series) is highly recommended.
1. Extract the contents of this .tar.bz2 file.
2. Change to the 'azureus' directory where the files were extracted.
3. Start Azureus by running the script named 'azureus'; ex. "./azureus"
If you have the Java JRE installed somewhere unusual (or not in your PATH),
use the JAVA_PROGRAM_DIR option in the script.
So instead of running ./azureus, I did "cd .." and then moved that azureus directory to /usr/local/bin (maybe not the best spot, but it's where I have been recommended to install programs.) I then created a symlink in /usr/bin called "azureus" which goes to /usr/local/bin/azureus/azureus.
I am running JRE 126.96.36.199, and /usr/lib/java/bin and /usr/lib/java/jre/bin are both in my path. One thing I have noticed is there are no .jar files in /usr/bin. Might this all be because I'm running azureus from the symlink in /usr/bin instead of the actual file itself in /usr/local/bin/azureus? I would try it myself, but I'm at work right now... there ARE a few .jar files in /usr/local/bin/azureus.